I think your list of schools are all reach schools and UW, UCI, UCSD may be matches. You mentioned that UCLA and Cal have big classes, so your parents are trying to sway you to avoid the big lecture halls. You should know that it’s not that different at UCI and UCSD. As a UW alum and even 20+ years ago, the classes at the UW thru about second quarter of sophomore year are also really, really large in size.
As an aside and not knowing your essays, etc., and only looking at what you listed, I think your ECs are on the lighter side unless you have a ton of depth with the ECs you listed. I’m not an admission official but based on stats I’ve seen, many of your listed schools will be super reach schools since your GPA and SAT scores hover below their 50%th.
You may want to consider other private schools like LMU, Pomona, Pepperdine, etc that are just as solid but may not be as selective.
For USC and Vanderbilt, apply before 12/1 so you can be considered for some of their merit $.